Observe that \(A\)  is a sum \(|I|\)  independent positive semi-definite random matrixes such that each summand has the operator norm equaling one.
Using the lower tail of the matrix Chernoff bound [1]} we have
\(\Pr (\lambda _{d}(A) \le \lambda _d(\operatorname{\mathbb {E}}A)/2) \le d(2e^{-1})^{{I}(d^{-1} + (d^{3/2} + d)^{-1})/2},\) 
